There is a popular paradox in mechanics--viz., "a body having a tendency to fall by its own weight, may be prevented from falling by adding to it a weight on the same side on which it tends to fall," and the paradox is demonstrated by another well-known child"s toy as depicted in the next cut.
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[Ill.u.s.tration: Fig. 48. The line of direction falling beyond the base; the bent wire and lead weight throwing the centre of gravity under the table and near the leaden weight; the hind legs become the point of support, and the toy is perfectly balanced.]
[Ill.u.s.tration: Fig. 49.--No. 1. Sword balanced on handle: the arc from C to D is very small, and if the centre, C, falls out of the line of direction it is not easily restored to the upright position.
No 2. Sword balanced on the point: the arc from C to D much larger, and therefore the sword is more easily balanced.]
After what has been explained regarding the improvement of the stability of the egg by lowering the situation of the centre of gravity, it may at first appear singular that a stick loaded with a weight at its upper extremity can be balanced perpendicularly with greater ease and precision than when the weight is lower down and nearer the hand; and that a sword can be balanced best when the hilt is uppermost; [Page 38]
but this is easily explained when it is understood that with the handle downwards a much smaller arc is described as it falls than when reversed, so that in the former case the balancer has not time to re-adjust the centre, whilst in the latter position the arc described is so large that before the sword falls the centre of gravity may be restored within the line of direction of the base.
[Ill.u.s.tration: Fig. 50.--No. 1. The two pieces of mahogany, carved to represent a man and a boy, one being 10 and the other 5 inches long, attached to board by hinges at H H.]
[Ill.u.s.tration: Fig. 51.--No. 2. The board pushed forward, striking against a nail, when the short piece falls first, and the long one second.]
For the same reason, a child tripping against a stone will fall quickly; whereas, a man can recover himself; this fact can be very nicely shown by fixing two square pieces of mahogany of different lengths, by hinges on a flat base or board, then if the board be pushed rapidly forward and struck against a lead weight or a nail put in the [Page 39] table, the short piece is seen to fall first and the long one afterwards; the difference of time occupied in the fall of each piece of wood (which may be carved to represent the human figure) being clearly denoted by the sounds produced as they strike the board.
Boat-accidents frequently arise in consequence of ignorance on the subject of the centre of gravity, and when persons are alarmed whilst sitting in a boat, they generally rise suddenly, raise the centre of gravity, which falling, by the oscillation of the frail bark, outside the line of direction of the base, cannot be restored, and the boat is upset; if the boat were fixed by the keel, raising the centre of gravity would be of little consequence, but as the boat is perfectly free to move and roll to one side or the other, the elevation of the centre of gravity is fatal, and it operates just as the removal of the lead would do, if changed from the base to the head of the "tombola" toy.
A very striking experiment, exhibiting the danger of rising in a boat, may be shown by the following model, as depicted at Nos. 1 and 2, figs.
52 and 53.
[Ill.u.s.tration: Fig. 52.--No. 1. Sections of a toy-boat floating in water. B B B. Three bra.s.s wires placed at regular distances and screwed into the bottom of the boat, with cuts or slits at the top so that when the leaden bullets, L L L, which are perforated and slide upon them like beads, are raised to the top, they are retained by the bra.s.s cuts springing out; when the bullets are at the bottom of the lines they represent persons sitting in a boat, as shown in the lower cuts, and the centre of gravity will be within the vessel.]
We thus perceive that the stability of a body placed on a base depends upon the position of the line of direction and the height of the centre of gravity.
Security results when the line of direction falls within the base.
Instability when just at the edge. Incapability of standing when falling without the base.
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[Ill.u.s.tration: Fig. 53.--No. 2. The leaden bullets raised to the top now show the result of persons suddenly rising, when the boat immediately turns over, and either sinks or floats on the surface with the keel upwards.]
[Ill.u.s.tration: Fig. 54. F. Board cut and painted to represent the leaning-tower of Pisa. G. The centre of gravity and plummet line suspended from it. H. The hinge which attaches it to the base board. I.
The string, sufficiently long to unwind and allow the plummet to hang outside the base, so that, when cut, the model falls in the direction of the arrow.]
The leaning-tower of Pisa is one hundred and eighty-two feet in height, and is swayed thirteen and a half feet from the perpendicular, but yet remains perfectly firm and secure, as the line of direction falls considerably within the base. If it was of a greater alt.i.tude it could no longer stand, because the centre of gravity would be so elevated that the line of direction would fall outside the base. This fact may be ill.u.s.trated by taking a board several feet in length, and having cut [Page 41] it out to represent the architecture of the leaning-tower of Pisa, it may then be painted in distemper, and fixed at the right angle with a hinge to another board representing the ground, whilst a plumb-line may be dropped from the centre of gravity; and it may be shown that as long as the plummet falls within the base, the tower is safe; but directly the model tower is brought a little further forward by a wedge so that the plummet hangs outside, then, on removing the support, which may be a piece of string to be cut at the right moment, the model falls, and the fact is at once comprehended.
The leaning-towers of Bologna are likewise celebrated for their great inclination; so also (in England) is the hanging-tower, or, more correctly, the ma.s.sive wall which has formed part of a tower at Bridgenorth, Salop; it deviates from the perpendicular, but the centre of gravity and the line of direction fall within the base, and it remains secure; indeed, so little fears are entertained of its tumbling down, that a stable has been erected beneath it.
[Ill.u.s.tration: Fig. 55.--No. 1. Two billiard-cues arranged for the experiment and fixed to a board: the ball is rolling _up_.
No. 2. Sections showing that the centre of gravity, C, is higher at A than at B, which represents the thick end of the cues; it therefore, in effect, rolls down hill.]
One of the most curious paradoxes is displayed in the ascent of a billiard-ball from the thin to the thick ends of two billiard-cues placed at an angle, as in our drawing above; here the centre of gravity is raised at starting, and the ball moves in consequence of its actually _falling_ from the high to the low level.
Much of the stability of a body depends on the height through which the centre of gravity must be elevated before the body can be overthrown.
The greater this height, the greater will be the immovability of the ma.s.s. One of the grandest examples of this fact is shown in the ancient Pyramids; and whilst gigantic palaces, with vast columns, [Page 42] and all the solid grandeur belonging to Egyptian architecture, have succ.u.mbed to time and lie more or less prostrate upon the earth, the Pyramids, in their simple form and solidity, remain almost as they were built, and it will be noticed, in the accompanying sketch, how difficult, if not impossible, it would be to attempt to overthrow bodily one of these great monuments of ancient times.
[Ill.u.s.tration: Fig. 56. C. Centre of gravity, which must be raised to D before it can be overthrown.]
[Ill.u.s.tration: Fig. 57. No. 1. The centre of gravity is near the ground, and falls within the wheels. No. 2. The centre of gravity is much elevated, and the line of direction is outside the wheels.]
The principles already explained are directly applicable to the construction or secure loading of vehicles; and in proportion as the centre of gravity is elevated above the point of support (that is, the wheels), so is the insecurity of the carriage increased, and the contrary takes place if the centre of gravity is lowered. Again, if a waggon be loaded [Page 43] with a very heavy substance which does not occupy much s.p.a.ce, such as iron, lead, or copper, or bricks, it will be in much less danger of an overthrow than if it carries an equal weight of a lighter body, such as pockets of hops, or bags of wool or bales of rags.
In the one instance, the centre of gravity is near the ground, and falls well within the base, as at No. 1, fig. 57. In the other, the centre of gravity is considerably elevated above the ground, and having met with an obstruction which has raised one side higher than the other, the line of direction has fallen outside the wheels, and the waggon is overturning as at No. 2.
The various postures of the human body may be regarded as so many experiments upon the position of the centre of gravity which we are every moment unconsciously performing.
To maintain an erect position, a man must so place his body as to cause the line of direction of his weight to fall within the base formed by his feet.
[Ill.u.s.tration: Fig. 58.]
The more the toes are turned outwards, the more contracted will be the base, and the body will be more liable to fall backwards or forwards; and the closer the feet are drawn together, the more likely is the body to fall on either side. The acrobats, and so-called "India-Rubber Brothers", dancing dogs, &c., unconsciously acquire the habit of accurately balancing themselves in all kinds of strange positions; but as these accomplishments are not to be recommended to young people, some other marvels (such as balancing a pail of water on a stick laid upon a table) may be adduced, as ill.u.s.trated in fig. 59.
Let A B represent an ordinary table, upon which place a broomstick, C D, so that one-half shall lay upon the table and the other extend from [Page 44] it; place over the stick the handle of an empty pail (which may possibly require to be elongated for the experiment) so that the handle touches or falls into a notch at H; and in order to bring the pail well under the table, another stick is placed in the notch E, and is arranged in the line G F E, one end resting at G and the other at E.
Having made these preparations, the pail may now be filled with water; and although it appears to be a most marvellous result, to see the pail apparently balanced on the end of a stick which may easily tilt up, the principles already explained will enable the observer to understand that the centre of gravity of the pail falls within the line of direction shown by the dotted line; and it amounts in effect to nothing more than carrying a pail on the centre of a stick, one end of which is supported at E, and the other through the medium of the table, A B.
[Ill.u.s.tration: Fig. 59.]
This ill.u.s.tration may be modified by using a heavy weight, rope, and stick, as shown in our sketch below.
[Ill.u.s.tration: Fig. 60.]
Before we dismiss this subject it is advisable to explain a term referring to a very useful truth, called the centre of percussion; a knowledge of which, gained instinctively or otherwise, enables the workman to wield his tools with increased power, and gives greater force to the cut of the swordsman, so that, with some physical strength, he may perform the feat of cutting a sheep in half, cleaving a bar of lead, or [Page 45] neatly dividing, _a la Saladin_, in ancient Saracen fashion, a silk handkerchief floating in the air. There is a feat, however, which does not require any very great strength, but is sufficiently startling to excite much surprise and some inquiry--viz., the one of cutting in half a broomstick supported at the ends on tumblers of water without spilling the water or cracking or otherwise damaging the gla.s.s supports.
[Ill.u.s.tration: Fig. 61.]
These and other feats are partly explained by reference to time: the force is so quickly applied and expended on the centre of the stick that it is not communicated to the supports; just as a bullet from a pistol may be sent through a pane of gla.s.s without shattering the whole square, but making a clean hole through it, or a candle may be sent through a plank, or a cannon-ball pa.s.s through a half opened door without causing it to move on its hinges. But the success of the several feats depends in a great measure on the attention that is paid to the delivery of the blows at the _centre of percussion_ of the weapon; this is a point in a moving body where the percussion is the greatest, and about which the impetus or force of all parts is balanced on every side. It may be better understood by reference to our drawing below. Applying this principle to a model sword made of wood, cut in half in the centre of the blade, and then united with an elbow-joint, the handle being fixed to a board by a wire pa.s.sed through it and the two upright pieces of wood, the fact is at once apparent, and is well shown in Nos. 1, 2, 3, fig. 62.
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[Ill.u.s.tration: Fig. 62. No. 1, is the wooden sword, with an elbow-joint at C. No. 2. Sword attached to board at K, and being allowed to fall from any angle shown by dotted-line, it strikes the block, W, outside the centre of percussion, P, and as there is unequal motion in the parts of the sword it bends down (or, as it were, breaks) at the elbow-joint, C.
No. 3 displays the same model; but here the blow has fallen on the block, W, precisely at the centre of percussion of the sword, P, and the elbow-joint remains perfectly firm.]
When a blow is not delivered with a stick or sword at the centre of percussion, a peculiar jar, or what is familiarly spoken of as a _stinging_ sensation, is apparent in the hand; and the cause of this disagreeable result is further elucidated by fig. 63, in which the post, A, corresponds with the handle of the sword.
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[Ill.u.s.tration: Fig. 63. A. The post to which a rope is attached. B and C are two horses running round in a circle, and it is plain that B will not move so quick as C, and that the latter will have the greatest moving force; consequently, if the rope was suddenly checked by striking against an object at the centre of gravity, the horse C would proceed faster than B, and would impart to B a backward motion, and thus make a great strain on the rope at A. But if the obstacle were placed so as to be struck at a certain point nearer C, viz., at or about the little star, the tendency of each horse to move on would balance and neutralize the other, so that there would be no strain at A. The little star indicates the _centre of percussion_.]
All military men, and especially those young gentlemen who are intended for the army, should bear in mind this important truth during their sword-practice; and with one of Mr. Wilkinson"s swords, made only of the very best steel, they may conquer in a chance combat which might otherwise have proved fatal to them. To Mr. Wilkinson, of Pall Mall, the eminent sword-cutler, is due the great merit of improving the quality of the steel employed in the manufacture of officers" swords; and with one of his weapons, the author has repeatedly thrust through an iron plate about one-eighth of an inch in thickness without injuring the point, and has also bent one nearly double without fracturing it, the perfect elasticity of the steel bringing the sword straight again. These, and other severe tests applied to Wilkinson"s swords, show that there is no reason why an officer should not possess a weapon that will bear comparison with, nay, surpa.s.s, the far-famed _Toledo_ weapon, instead of submitting to mere army-tailor swords, which are often little better than hoops of beer barrels; and, in dire combat with Hindoo or Mussulman fanatics" Tulwah, may show too late the folly of the owner.
[Ill.u.s.tration: Fig. 64.]
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